Question

find all local maxima and minima (the y-values) and the vales where they occur

g(x) x absolute value 2x+5 absolute value

Answer 1

"g(x) x absolute value 2x+5 absolute value"

is not very clear to me.

Is it
g1(x)= |x|*|2x+5|, or is it
g2(x)= x*|2x+5|, or is it something else?

Usually the absolute function makes a kink when the expression becomes negative, and hence produces a local maximum or minimum.